Effects of phase relative motion on critical bubbly flows through a converging-diverging nozzle

One-dimensional bubbly flows through converging-diverging nozzles are investigated using a two-fluid model. Effects associated with both translational and radial relative motions between bubbles and liquid are incorporated. Calculation of a subsonic case is performed first and shows good agreement with experiments. The model is then applied to critical (or choked) flow situations studied previously by Muir and Eichhorn. In their experiments, Muir and Eichhorn found larger critical pressure ratios (which are defined as the ratios of the throat pressure to the pressure upstream of the nozzle under choked conditions) and mass flow rates than homogeneous flow theory. They measured significant slip between phases which, therefore, was speculated to be responsible for these discrepancies. It is demonstrated in this paper that the phase relative velocity can be predicted reasonably well (within the experimental uncertainty) using the present model. Excellent agreement between the predicted critical mass flow rates and the experimental data is obtained. However, compensation for the critical pressure ratios is not apparent. Other important natures of the critical flows are also explored, including the formation of compression shock waves present in the divergent part of the nozzle. Our computations show that the pressure ratios across the shocks agree very well with the Hugoniot relation established by Thang and Davis.